Under broad hypotheses we derive a scalar reduction of the generalized Kähler-Ricci soliton system.We realize solutions as critical points of a functional,analogous to the classical Aubin energy,defined on an orb...Under broad hypotheses we derive a scalar reduction of the generalized Kähler-Ricci soliton system.We realize solutions as critical points of a functional,analogous to the classical Aubin energy,defined on an orbit of the natural Hamiltonian action of diffeomorphisms,thought of as a generalized Kähler class.This functional is convex on a large set of paths in this space,and using this we show rigidity of solitons in their generalized Kähler class.As an application we prove uniqueness of the generalized Kähler-Ricci solitons on Hopf surfaces constructed in Streets and Ustinovskiy[Commun.Pure Appl.Math.74(9),1896-1914(2020)],finishing the classification in complex dimension 2.展开更多
The present work concerns the numerical approximation of the M_(1) model for radiative transfer.The main purpose is to introduce an accurate finite volume method according to the nonlinear system of conservation laws ...The present work concerns the numerical approximation of the M_(1) model for radiative transfer.The main purpose is to introduce an accurate finite volume method according to the nonlinear system of conservation laws that governs this model.We propose to derive an HLLC method which preserves the stationary contact waves.To supplement this essential property,the method is proved to be robust and to preserve the physical admissible states.Next,a relevant asymptotic preserving correction is proposed in order to obtain a method which is able to deal with all the physical regimes.The relevance of the numerical procedure is exhibited thanks to numerical simulations of physical interest.展开更多
In this work,we prove an optimal global-in-time L^(p)-L^(q) estimate for solutions to the Kramers-Fokker-Planck equation with short range potential in dimension three.Our result shows that the decay rate as t-→+∞ is...In this work,we prove an optimal global-in-time L^(p)-L^(q) estimate for solutions to the Kramers-Fokker-Planck equation with short range potential in dimension three.Our result shows that the decay rate as t-→+∞ is the same as the heat equation in x-variables and the divergence rate as t→O_(+) is related to the sub-ellipticity with loss of one third derivatives of the Kramers-Fokker-Planck operator.展开更多
基金V.A.was supported in part by an NSERC Discovery Grant and a Connect Talent Grant of the Région Pays de la Loire.
文摘Under broad hypotheses we derive a scalar reduction of the generalized Kähler-Ricci soliton system.We realize solutions as critical points of a functional,analogous to the classical Aubin energy,defined on an orbit of the natural Hamiltonian action of diffeomorphisms,thought of as a generalized Kähler class.This functional is convex on a large set of paths in this space,and using this we show rigidity of solitons in their generalized Kähler class.As an application we prove uniqueness of the generalized Kähler-Ricci solitons on Hopf surfaces constructed in Streets and Ustinovskiy[Commun.Pure Appl.Math.74(9),1896-1914(2020)],finishing the classification in complex dimension 2.
文摘The present work concerns the numerical approximation of the M_(1) model for radiative transfer.The main purpose is to introduce an accurate finite volume method according to the nonlinear system of conservation laws that governs this model.We propose to derive an HLLC method which preserves the stationary contact waves.To supplement this essential property,the method is proved to be robust and to preserve the physical admissible states.Next,a relevant asymptotic preserving correction is proposed in order to obtain a method which is able to deal with all the physical regimes.The relevance of the numerical procedure is exhibited thanks to numerical simulations of physical interest.
文摘In this work,we prove an optimal global-in-time L^(p)-L^(q) estimate for solutions to the Kramers-Fokker-Planck equation with short range potential in dimension three.Our result shows that the decay rate as t-→+∞ is the same as the heat equation in x-variables and the divergence rate as t→O_(+) is related to the sub-ellipticity with loss of one third derivatives of the Kramers-Fokker-Planck operator.
